Findings from the Human Genome Project highlight the intricacy of interactions between cell regulation, genes and proteins. It is generally understood that biological functions and biological activities are controlled by subsets of genes interacting with proteins in a highly controlled manner. High throughput technologies such as microarrays are valuable for studying a large number of biological components simultaneously, but sound conclusions from these technologies depend on appropriate statistical analyses of the genomic/proteomic data. The long-term objective of this proposal is to develop appropriate statistical tools to explore gene/protein interactions and to discover how these interactions function in biological activities (e.g. induction of disease phenotype). This proposal concerns the analysis of short oligonucleotide data, as in GeneChip studies and exon tiling arrays. Low-rank approximations to the expression data matrices play a central role in the proposed research. The specific aims are: (1) to develop a fast and robust low-rank algorithm to perform low-rank approximation to a data matrix that is subject to outliers;(2) to develop diagnostic tools and statistical tests for determining whether a low-rank representation is adequate to capture gene expression profiles;(3) to develop both nonparametric and likelihood-based approaches for flagging and detecting alternative splicing with exon tiling arrays. Singular value decomposition is a starting point for the proposed work towards those specific aims. Alternating robust (outlier resistant) regression methods will be used for Aims (1) and (3). Likelihood- based and data adaptive methods will be developed for Aims (2) and (3). The proposed research distinguishes itself from most of the existing statistical work on microarray data, as it focuses on probe-level rather than gene-level data. The investigators believe that the standard uni-dimensional summary of gene expression data could lead to loss of important information.